
(* ::Section:: *)
(* Tdec *)


(* ::Text:: *)
(*`Tdec[{{qi, mu}, {qj, nu}, ...}, {p1, p2, ...}]` calculates the tensorial decomposition formulas for Lorentzian integrals. The more common ones are saved in `TIDL`.*)


(* ::Subsection:: *)
(* See also *)


(* ::Text:: *)
(*TID, TIDL, OneLoopSimplify.*)


(* ::Subsection:: *)
(* Examples *)


(* ::Text:: *)
(*Check that $\int d^D f(p,q) q^{\mu}= \frac{p^{\mu}}{p^2} \int d^D f(p,q) p \cdot q$*)


Tdec[{q,\[Mu]},{p}]
%[[2]]/.%[[1]]


(* ::Text:: *)
(*This calculates integral transformation for any $\int d^D q_1 d^D q_2 d^D q_3$ $f(p,q_1,q_2,q_3) q_1^{\mu} q_2^{\nu}q_3^{\rho}$.*)


Tdec[{{Subscript[q, 1],\[Mu]},{Subscript[q, 2],\[Nu]},{Subscript[q, 3],\[Rho]}},{p},List->False]
Contract[% FVD[p,\[Mu]]FVD[p,\[Nu]] FVD[p,\[Rho]]]//Factor



